Nilai \( \displaystyle \lim_{x\to b} \ \frac{\sin x - \sin b}{x - b} = \cdots \)
Pembahasan:
\begin{aligned} \lim_{x\to b} \ \frac{\sin x - \sin b}{x - b} &= \lim_{x\to b} \ \frac{2 \cos \frac{1}{2} (x+b) \sin \frac{1}{2} (x-b)}{x-b} \\[8pt] &= \lim_{x\to b} \ \frac{\cos \frac{1}{2} (x+b) \sin \frac{1}{2} (x-b)}{\frac{1}{2}(x-b)} \\[8pt] &= \lim_{x\to b} \ \cos \frac{1}{2} (x+b) \cdot \lim_{x\to b} \ \frac{\sin \frac{1}{2} (x-b)}{\frac{1}{2}(x-b)} \\[8pt] &= \cos \frac{1}{2} (b+b) \cdot 1 \\[8pt] &= \cos b \end{aligned}